the graph shows quadrilaterals cdef and rstu. is cdef congruent to rstu? justify your answer. yes, because a reflection across the y - axis maps cdef onto rstu. yes, because a rotation 90° clockwise around the origin maps cdef onto rstu. no, because $ \overline { fc } $ and $ \overline { ur } $ do not have the same length. no, because $ \overline { de } $ and $ \overline { st } $ do not have the same length.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{DE} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For points $ D(9,-5) $ and $ E(6,-2) $, $ x_1 = 9,y_1=-5,x_2 = 6,y_2=-2 $.
$$
\begin{align*}
d_{DE}&=\sqrt{(6 - 9)^2+(-2+5)^2}\
&=\sqrt{(-3)^2+3^2}\
&=\sqrt{9 + 9}\
&=\sqrt{18}=3\sqrt{2}
\end{align*}
$$
## Step2: Calculate the length of $ \overline{ST} $
For points $ S(-8,-5) $ and $ T(-6,-2) $, $ x_1=-8,y_1 = -5,x_2=-6,y_2=-2 $.
$$
\begin{align*}
d_{ST}&=\sqrt{(-6 + 8)^2+(-2 + 5)^2}\
&=\sqrt{2^2+3^2}\
&=\sqrt{4+9}\
&=\sqrt{13}
\end{align*}
$$
Since $ 3\sqrt{2}
eq\sqrt{13} $, $ \overline{DE} $ and $ \overline{ST} $  do not have the same length. Congruent figures have all corresponding sides equal.

# Answer:
No, because $ \overline{DE} $ and $ \overline{ST} $ do not have the same length.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \( \overline{DE} \)

Step2: Calculate the length of \( \overline{ST} \)

Answer: